FA2015 Torispherical Head

BULLETIN

FEATURE

 A Review of ASME Code Section VIII, Division 1, Torispherical Head Calculations BY TIM GARDNER, SENIOR STAFF ENGINEER

T

he inspector can encounter many types of heads when inspecting pressure vessels. Examples include hemispherical, ellipsoidal, at, and torispherical heads to name a few. Most of the general public is familiar with hemispherical, ellipsoidal (three-dimensional version of an ellipse), and at shapes but the torispherical head is relatively unknown to those without an inspection or fabrication background. Even E ven so, torispherical heads are among the most commonly chosen heads by manufacturers for use in the construction of pressure vessels. There are two things that dierentiate torispherical heads from other heads used in The American Society of Mechanical Engineers’ Boiler and Pressure Vessel Code (ASME Code) Section VIII, Division Division 1, construction. The rst is that the spherically dished, or torispherical, head is one of the most confusing when it comes to its geometry.. The second involves performing etry calculations of thickness or allowable pressure. Knowing which equations to use depending on the dimensions, and how to deal with corrosion and its particular eects on the head hea d geometry, is more dicult than one might think. Let’s examine the characteristics of this head and review the pressure or thickness calculations to alleviate the confusion for the inspector and ensure that this critical vessel component is given the proper scrutiny so that it meets or exceeds the requirements of ASME Code Section VIII, Division 1.

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What is a Torispherical Head?

We rst will look at the unique physical characteristics of the torispherical head. See Figure 1 below showing showing an ASME Code Code Section VIII, Division Division 1, torispherical head with dened dimensions:

t L r Do

Spherically Dished ( Torispherical Head) Figure 1: Torispherical Head Dimensioned per ASME Code Section VIII, Division 1

Where DO  e eer    he e r he r r= inside knuckle radius L= the inside spherical radius (crown radius) t= thickness of the head In many cases L=DO , and in no case will L be greater than DO. This leads leads to a very common question an inspector may ask in regard to this type of head: How can the inside crown radius radius equal the outside diameter? To answer this we need need to develop an understanding of just what a torispherical head is.  

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Donut Partial Sphere

Flange r

Do

L

Figure 2: Geometry of a Torispherical Head

A torispherical shape results when a portion of a sphere intersects a torus. Sphere is the formal term to describe a ball shape and torus is a geometric term describing the shape of a donut. If you picture a small portion of a ball resting on a donut and only look at the outside surface, you have a pretty good idea of what a torispherical shape looks like. See Figure 2 to better understand how the curvature of the torispherical head is determined. Next let’s consider the cross-section of the shape. The construction of this head can be best thought of in terms of the circles as shown in Figure 2. The arc associated with the majority of the head is part of a circle (cross-section of a sphere) with a radius of L. The arc associated with the knuckle radius is part of a much smaller circle (cross-section of the torus or donut) with a radius of r. The ange dimensions are generally selected to suit the design of the vessel to which the head attaches, but will always be the outside diameter of the torus shape. So how does an inspector use this information to verify torispherical head calculations?  

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BULLETIN

FEATURE

What is a UG-32(e) Torispherical Head and How is it Calculated?

Probably the most common of the torispherical heads encountered by inspectors is the Section VIII, UG-32(e) head. This class of torispherical heads has special dimensional relationships de ned in the UG-32(e) paragraph as follows: • • •

tS /L > 0.002, where tS is the minimum specied thickness after forming The inside knuckle radius is  of the inside crown radius or r=0.06L The inside crown radius equals the outside diameter of the skirt or L=DO

Calculations for the torispherical head, sometimes called a anged and dished (FD) head, when made according to ASME Section VIII, Division 1, UG-32(e), are relatively straightforward. To calculate the required thickness or allowable pressure of a UG-32(e) head, the following formulas are used: (1)

t = 0.885PL/( SE-0.1P)

P = SEt/(0.885L + 0.1t)

Where L and t are as dened on p. 20 P= Internal design pressure S= Maximum allowable stress in tension E= Lowest eciency for any joint in the head Determining the required thickness, t, or the allowable pressure, P, is a matter of inserting the S , E , L , and P or t values as appropriate. For a new vessel that will not be subject to corrosion, a thickness can be specied at or thicker than the calculated required value. But what about vessels where corrosion is expected and a corrosion factor has been applied? How is Corrosion Handled when ain Torispherical Head Calculations?

Corrosion occurs in some vessels due to the properties of the liquid or gas being contained. The vessel designer takes this into account by adding a corrosion allowance to the thickness of the shell, heads, and other components exposed to the substance. The corrosion allowance is documented on the vessel data report and is included as part of the thickness listed for the heads. Typically, the corrosion is assumed to be uniform for the head. Let’s look at what happens to a torispherical head as it corrodes. The inside crown radius and the knuckle radius both are changed as the material is corroded away. They are increased  by the amount of corrosion. If ” of material is corroded away, these two radii are increased by ” each. What does not change is the outside diameter of the ange or DO. So in the UG-32(e) head case, L is no longer equal to DO. If it exceeds DO then it violates the rule in UG-32(j) stating that L cannot be larger than DO. This means that if a torispherical head that was purchased with no allowance for corrosion is found with less than the expected thickness needed to ensure L is less than DO , it would no longer meet ASME Code Section VIII, Division 1 requirement. In addition, the knuckle radius is no longer 6  of the crown radius. In most cases it would be close to 6 , but mathematically it would be greater since the corrosion allowance would be added to both the top and bottom (numerator and denominator) of the fraction r/L. A torispherical head with geometry based on UG-32(e) still can be used for an application involving corrosion, but the corroded state would need to satisfy the UG-32(e) geometry. One would use the fully corroded values for calculating the

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thickness needed for the given pressure and then add an amount of thickness equivalent to the corrosion allowance to the required calculated thickness of the head to determine the minimum speci ed thickness. For example, the required fully corroded thickness of a UG-32(e) torispherical head for a given internal pressure is calculated to be ”. If the vessel manufacturer wishes to include a ” corrosion allowance, it would add ” thickness to all internal surfaces of the head. When purchasing or manufacturing the head, a thickness dimension of 1” reecting the extra thickness would be speci ed. In many cases the vessel designer will prepare a template of the new head contours for use by the receiving department. The knuckle radius that results from adding the extra thickness for corrosion will be smaller than 6 of the corrosionadjusted spherical radius and would, therefore, normally violate UG-32(j). Recall that UG-32(j) requires that the knuckle radius be greater or equal to .06 DO and in no case no less than three times the head thickness. This is not an issue since the dimensional symbols in the equations for calculating thickness or pressure are all based on values in the corroded state as stated in UG-16(e). The extra thickness need not be addressed in any code equations or rules. On the other hand, if a larger knuckle radius is used to avoid violating UG-32(j), then the head will corrode to a shape that does not satisfy the geometry of UG-32(e). So what about torispherical heads that do not conform to the geometry of UG-32(e)? How are Calculations Performed for Torispherical Heads Not Conforming to UG-32(e)?

There are other torispherical heads that are not designed to the UG-32(e) conguration. Other torispherical heads that inspectors may encounter include the 80-10 torispherical head and the high crown type. For 80-10 heads, the dish radius is 80 of the outside diameter or L=0.8DO and the knuckle radius is 10 of the diameter. For the high crown torispherical head, the crown radius is 85 of the outside diameter. For these and other non-standard heads, the formula in ASME Code Section VIII, Division 1, Appendix 1-4, would need to be used to check for adequate thickness or allowable pressure. The Appendix 1-4 equations are stated in (2) below: (2)

t = PLM/(2SE-0.2P) or P = 2SEt/(LM+0.2t) where M = {3 + SQRT(L/r)}/4

The M value varies from 1 to 1.77. The 1.77 represents the case where r/L is 0.06, which is the limiting value per UG-32(j). The equation for thickness in (2) reduces to the equation for thickness in (1) for the case where r= 0.06L. A torispherical head with a knuckle radius of 0.06L results in the greatest required thickness for a given spherical or crown radius. As with the UG-32(e) calculation, the dimensional symbols are based on the fully corroded condition. The corrosion factor is handled the same way with the Appendix 1-4 designed heads as with UG-32(e) designed heads. Once the head thickness is calculated, the corrosion factor is added to the calculated thickness. The limits on the knuckle radius and the dish radius in UG-32(j) are applicable for these and any other ASME torispherical heads. Conclusion

It is important that an inspector properly verify the design of torispherical heads. The inspector should also review receiving records for the head to ensure that the proper head was received and was con rmed to have been made to the specied dimensions and shape. When manufacturers and inspectors understand how the standard ASME Code Section VIII, Division 1, UG-32(e), and other types of torispherical heads are designed, dimensioned, and calculated, they can ensure that the heads are in compliance. This will result in a pressure vessel head that will perform as expected and ensure the pressure integrity of the vessel during its service life.  

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